Long-wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid

Abstract

The high frequency limits of the singular component A(ω) of the small wavevector expansion of the longitudinal (L) and transverse (T) components of the spin-resolved exchange-correlation kernel tensor fσσ ′ (q, ω) in a two-dimensional isotropic electron liquid with arbitrary spin polarization are studied. Here G L,T σσ ′ (q, ω) is the spin-resolved local field factor, v(q) is the Coulomb interaction in momentum space, and σ denotes spin. Particularly, the real part of A(ω) is found to be logarithmically divergent at large ω. The large wavevector structure of the corresponding spin-resolved static structure factor is also established.